CMB SLS one instant or over a period of time

My question is regarding when the the CMB was created. I understand that it is predicted to have been "when the universe cooled to about 3,000K". However, might it have been possible that different areas of the universe reached that temperature and decoupled a little earlier than others? This would mean there is some variation in the "Surface of Last Scattering" rather than being smooth.

The idea is that this might describe the anisotropies of the relic radiation. The cooler areas would indicate places that cooled and decoupled further in the past (earlier in the universe's time-line) and that the hotter areas would indicate areas that cooled and decoupled a little later.

My question is regarding when the the CMB was created. I understand that it is predicted to have been "when the universe cooled to about 3,000K". However, might it have been possible that different areas of the universe reached that temperature and decoupled a little earlier than others? This would mean there is some variation in the "Surface of Last Scattering" rather than being smooth.

The idea is that this might describe the anisotropies of the relic radiation. The cooler areas would indicate places that cooled and decoupled further in the past (earlier in the universe's time-line) and that the hotter areas would indicate areas that cooled and decoupled a little later.

If this were true, then there would be strong anisotropies in the CMB. There are not: it's nearly the same in every direction. The anisotropies that we do see are only one part in 100,000 (well, except for the dipole, which is around one part in 10,000, but then the dipole is likely explained by our movement, not anything intrinsic to the CMB).

Edit: As a slight caveat, it is indeed the case that different parts of the CMB cooled at slightly different times. This isn't the cause of the anisotropies, but is instead as a result of them. Parts that were warmer cooled later, while parts that were cooler cooled earlier. But not by much: these temperature differences were minuscule.

That should be a good start for some of the ideas. Things can get pretty involved pretty quickly and you also have to consider that you can have anisotropies generated at the time of the formation of the CMB as well as anisotropies created during the travel time of CMB photons (e.g. Gravitational lensing, foreground contaminations, Sunyaev-Zel'dovich and many more).

So are you saying that the anisotropies are or are not due to different areas cooling at different rates over a period of time?

Cooling at different rates? Definitely not. The laws of physics are the same everywhere, and the contents almost exactly the same. There are only tiny differences in density, with the more dense regions being of very slightly higher temperature, and the less dense regions being slightly lower.